PRP Records

Probable Primes Top 10000

(205869 PRPs in the top)


What is a PRP ?

A PRP is a probable prime number, a number that nobody knows how to prove or disprove its primality.
Here are some criterions that can be used to recognize these numbers :

- N does not have any prime factor up to 2^32.
- N cannot be trivially written into a product.
- Take 3 square-free consecutive bases such that (b1/N)=(b2/N)=(b3/N)= -1. N should be such that b1^((N-1)/2)=b2^((N-1)/2)=b3^((N-1)/2)= -1 (mod N).
- Take a prime base such that (b/N)= -1 and b<>b1<>b2<>b3. N should pass the strong test in base b.
- or more (if someone has got an idea) !!!


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1-250   251-500   501-750   751-1000   1001-1250   1251-1500   1501-1750   1751-2000   
2001-2250   2251-2500   2501-2750   2751-3000   3001-3250   3251-3500   3501-3750   3751-4000   
4001-4250   4251-4500   4501-4750   4751-5000   5001-5250   5251-5500   5501-5750   5751-6000   
6001-6250   6251-6500   6501-6750   6751-7000   7001-7250   7251-7500   7501-7750   7751-8000   
8001-8250   8251-8500   8501-8750   8751-9000   9001-9250   9251-9500   9501-9750   9751-10000   


Rank Probable prime Digits (> 30000) Who ? When ?
600113^66179+6673720Lelio R Paula01/2015
6002(82*10^73714-1)/973715Robert Price12/2014
6003(29*2^244856-1)/18612173706Lelio R Paula01/2014
6004(13*2^244840-1)/279973702Lelio R Paula01/2014
6005(13*10^73701+17)/373702Robert Price06/2015
6006(2^244787-1017)/2841173684Lelio R Paula07/2012
6007(3^154421-4)/2373677Lelio R Paula06/2012
60088*7^87170+573669Lelio R Paula10/2014
6009(29*10^73659-113)/373660Robert Price11/2017
6010Phi(40100,-40100)73651Henri Lifchitz06/2013
6011(4*10^73647-19)/373648Robert Price06/2017
60122^244618-229773638Yves Minet10/2009
60133*5^105344+873633Lelio R Paula10/2014
60145^105334-1409673626Enzo Doria02/2013
6015(2^244584-7)/1323707424303373614Lelio R Paula07/2012
60162^244465-11018573592Enzo Doria05/2014
60172^244443+4075573585Lelio R Paula05/2013
60182^244404+384173573Yves Minet03/2011
60192^244372-11062773564Enzo Doria05/2014
6020(3*2^244255+1)/24573527Lelio R Paula08/2012
6021(11*2^244245+1)/2373525Lelio R Paula08/2012
6022(15185*2^244187-1)/611173509Lelio R Paula04/2015
6023(91^37507+1)/9273476Paul Bourdelais08/2017
602418^58521+6573460Lelio R Paula01/2015
602513^65940+3673454Lelio R Paula01/2015
6026(625^26267+1)/62673437Richard Fischer12/2017
60275^105050-1473427Lelio R Paula08/2014
6028(((((((((((((30201^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-273401Serge Batalov07/2016
602915^62410-4673400Lelio R Paula01/2015
60302^243733+186970773371Enzo Doria05/2016
603111^70439-543073355Enzo Doria01/2013
60322^243676-8773354Lelio R Paula03/2012
6033(101*10^73346-17)/373348Robert Price08/2016
60342^243621-11318573338Enzo Doria07/2014
6035(5*2^243610-1)/166973332Lelio R Paula01/2014
60362*5^104888-773314Lelio R Paula10/2014
6037(58695*2^243516-1)/98373308Lelio R Paula04/2015
6038(3^153648-2)/3342313809773299Lelio R Paula06/2012
603918^58376-525573278Enzo Doria03/2013
604011^70363+3273276Lelio R Paula02/2015
60412^243413+425773275Lelio R Paula05/2013
6042104824^5+5^10482473269Andrey Kulsha07/2010
60437^86689-6^8668973261Predrag Minovic09/2004
60442^243296+9019573240Lelio R Paula05/2013
6046p(15433)#/2-473218Robert Price12/2016
6045(59*10^73217-77)/973218Robert Price11/2017
60472^243127+7135573189Lelio R Paula05/2013
60482^243116-24941973186Paul Bourdelais03/2013
6049(58695*2^243085-1)/1173180Lelio R Paula04/2015
605011^70262-9873171Lelio R Paula02/2015
6051(2^243034+47)/72270330373152Lelio R Paula07/2012
6052(2^242966+47)/4688773136Lelio R Paula07/2012
6053(43^44773-1)/4273134Robert Price04/2014
60546^93980-15835973131Mike Oakes02/2011
60556^93915+5373081Lelio R Paula01/2015
6056(5*10^73079+211)/973079Robert Price12/2017
6057(74*10^73076+43)/973077Robert Price10/2015
6058(3^153125+2)/114495573054Lelio R Paula06/2012
60592^242632-11219973040Enzo Doria06/2014
6060V(351646)73029Serge Batalov03/2015
606118^58175-8573026Lelio R Paula01/2015
6062p(15395)#/2-473019Robert Price12/2016
6063(4^121271+3^121271)/773012Jean-Louis Charton03/2011
60648*6^93825-573011Lelio R Paula10/2014
6066(F(220)^1601-F(219)^1601)/F(218)73005Wayne Halsdorf08/2013
6065(73^39181+1)/7473005Paul Bourdelais08/2017
60676^93815+14373003Lelio R Paula01/2015
60686^93812+573000Wojciech Florek03/2006
606919^57078-6272989Lelio R Paula01/2015
6070(29*10^72985+91)/372986Robert Price03/2016
607111^70082-252072983Enzo Doria12/2012
60726^93773+13372970Lelio R Paula01/2015
60732^242328-5972948Lelio R Paula03/2012
60745^104358-1301672944Enzo Doria02/2013
6075(75*10^72941-57)/9972941Ray Chandler03/2011
607612^67585-9572937Lelio R Paula02/2015
60772^242230-11328572919Enzo Doria07/2014
6078(5*10^72916-11)/372917Erik Branger12/2013
60792^242220-11039972916Enzo Doria05/2014
60802^242205-11341372911Enzo Doria07/2014
6081(3^152809+3^76405+1)/772908Serge Batalov03/2014
60822^242175+7424372902Yves Minet03/2011
60832^242150+1765972895Lelio R Paula11/2009
608411^69982-234072879Enzo Doria12/2012
6085(23*2^242093+1)/1011772875Lelio R Paula08/2012
6086(67607*2^242043+1)/3326372863Lelio R Paula06/2014
60872^242032+8772859Lelio R Paula03/2012
60882^241968-11059572840Enzo Doria05/2014
6089(10^72821+71)/972821Robert Price11/2014
60902^241852-6487572805Lelio R Paula05/2013
6091F(348307)/2056289086590809372776Donovan Johnson07/2007
6092(67*10^72772+23)/972773Ray Chandler11/2010
6093(8*10^72759+67)/372760Robert Price01/2017
60942^241670+14572750Lelio R Paula03/2012
60955^104074+5272745Lelio R Paula08/2014
6096(3^152466-5)/72472742Lelio R Paula06/2012
609720^55908-4172738Lelio R Paula01/2015
6098(73*10^72735+53)/972736Robert Price10/2015
609910^72730+22401172731Patrick De Geest05/2013
610010^72730-9972730Robert Price05/2011
61013*10^72723+6772724Robert Price11/2017
6102(11^69833+3^69833)/1472723Robert Price03/2013
6103(10^72723-79)/372723Robert Price10/2017
6104(88*10^72711-43)/972712Robert Price11/2015
61053^152379+28072704Lelio R Paula01/2015
6106(25*10^72703-241)/972704Robert Price01/2017
6107(47*10^72696+133)/972697Robert Price04/2017
610817^59077-9072692Lelio R Paula01/2015
610965^40096+5872691Lelio R Paula01/2016
6110(29*2^241446-1)/24572682Lelio R Paula01/2014
611211^69783-3840000072672Enzo Doria01/2013
61112^241409-11290372672Enzo Doria06/2014
6113(3^152287+1)/472659Paul Bourdelais04/2008
61143^152249-5672642Lelio R Paula01/2015
611510^72631+3772632Robert Price01/2011
611610^72631-881372631Patrick De Geest05/2013
6117(19*2^241254+1)/10172624Lelio R Paula08/2012
6118(9^76103+8^76103)/1772620Robert Price12/2012
61192^241220-11233772615Enzo Doria06/2014
6120(82*10^72612+449)/972613Robert Price02/2017
61212^241169-1579372600Enzo Doria04/2013
61229*10^72595+1172596Robert Kinser01/2017
6123(25*2^241048+1)/8972563Lelio R Paula08/2012
6124(22*10^72560+17)/372561Robert Price09/2015
61252^241032-2372558Lelio R Paula02/2012
612634485*10^72550+2^241004-372555Gilbert Mozzo12/2012
61272^241004-372550M. Frind & P. Underwood07/2002
612897*10^72522-372524Robert Price01/2017
6129(68*10^72516+7)/372518Robert Price03/2016
6130(78557*2^240844+1)/6372505Lelio R Paula06/2014
613167^39701-6672497Norbert Schneider11/2014
6132(185*10^72484+7)/372486Robert Price02/2017
6134(293*27^50631-1736)/1372473Curtis Bright05/2015
6133103^36005-10272473Norbert Schneider10/2016
613515^61616+8872467Lelio R Paula01/2015
613645^43831+272462Lelio R Paula05/2013
61372^240692-49238972456Paul Bourdelais03/2013
6138(646*10^72446-7)/972448Robert Price07/2016
61399*6^93083+772434Lelio R Paula10/2014
61402^240617-364572433Lelio R Paula05/2013
614111^69531-2400072410Enzo Doria12/2012
6142(22699*2^240396+1)/5572370Lelio R Paula06/2014
61436^92995+1372365Lelio R Paula01/2015
6144(11*10^72362-149)/372363Robert Price01/2017
6145(2^240381+3)/5165572358Lelio R Paula05/2012
61466^92974-5572348Lelio R Paula01/2015
61472^240295+1172337Lelio R Paula02/2012
6148(14*10^72326-53)/372327Robert Price12/2016
614915^61493-4672322Lelio R Paula01/2015
6150lucasU(46,1,43497)-lucasU(46,1,43496)72315Mike Oakes04/2009
61515*10^72302+972303Dmitry Domanov11/2010
6152(9787*2^240179-1)/26572303Lelio R Paula04/2015
615311^69419-312072293Enzo Doria12/2012
61544*10^72274-8372275Robert Price10/2017
615510^72267+3372268Robert Price01/2011
615610^72267-55394772267Patrick De Geest05/2013
615711^69389-138072262Enzo Doria12/2012
6158(16^60013-5^60013)/1172262Robert Price07/2013
61597^85507-3072262Lelio R Paula08/2014
6160(19*2^240026-1)/1572256Lelio R Paula02/2014
6161(3^151426-2)/66133772243Lelio R Paula06/2012
6162gcd(V(1296375),5*F(259275)*(F(259275)-1)+1)72227Serge Batalov04/2015
61632^239863-11226772206Enzo Doria06/2014
61642^239853-11485372203Enzo Doria05/2015
6165(4*10^72174+149)/972174Robert Price03/2017
6167(2^239671+9)/29613172143Lelio R Paula05/2012
61662^239651-11066572143Enzo Doria05/2014
6168(29*2^239650-1)/330572140Lelio R Paula01/2014
6169241^30280+30280^24172128Norbert Schneider11/2014
6170(68*10^72120-23)/972121Robert Price10/2015
6171(9^75571+8^75571)/1772112Robert Price12/2012
6172(15*2^239530-1)/17372105Lelio R Paula01/2014
61732^239513-11251972101Enzo Doria06/2014
6174(10^72097+149)/372097Serge Batalov12/2014
61752^239442-655572080Lelio R Paula05/2012
61762*5^103106+372069Lelio R Paula10/2014
61772^239402-19772068Lelio R Paula02/2012
61782^239356-11187572054Enzo Doria05/2014
6179(38*10^72050-119)/972051Robert Price11/2016
61802^239339+1501572049Lelio R Paula01/2013
6181159^32728+272048Lelio R Paula05/2013
618215^61259-3872047Lelio R Paula01/2015
618392^36683-91^3668372038Robert Price08/2015
61842^239280+5461572031Lelio R Paula05/2012
6185(47*2^239267+1)/7772027Lelio R Paula04/2015
6186(85*10^72025-1)/372027Robert Price07/2017
61872^239236-9730572018Lelio R Paula05/2012
61882^239169+5971998Lelio R Paula02/2012
6189lucasU(2010,1,21796)-lucasU(2010,1,21795)71994Mike Oakes05/2009
6190(15*2^239171-1)/10630171994Lelio R Paula01/2014
6191(29^49211-1)/2871965Robert Price04/2012
6192(299*10^71963+1)/371965Robert Price11/2017
6194L(344293)71953Renaud Lifchitz09/2003
6193V(344293)71953Serge Batalov03/2015
61956*10^71951+771952Dmitry Domanov11/2010
61963^150798+4071949Lelio R Paula01/2015
61972^238961+9571935Lelio R Paula02/2012
61982^238936-40771927Yves Minet02/2012
61992^238923-2863571923Lelio R Paula05/2012
620010^71910+2511971911Patrick De Geest05/2016
620110^71910-80171910Robert Price04/2016
62022^238845-11265171900Enzo Doria06/2014
62032^238792-11124571884Enzo Doria05/2014
62046*7^85059+571884Lelio R Paula10/2014
62052^238752-11058971872Enzo Doria05/2014
620612^66581+771853Lelio R Paula07/2014
6207(7*2^238691+1)/4122971850Lelio R Paula06/2012
62084*3^150568-571840Lelio R Paula04/2014
62096^92301+6771825Lelio R Paula01/2015
62102^238568+9876533171817Jason Earls01/2009
62112^238541-11272371808Enzo Doria06/2014
62122^238529-1594971805Enzo Doria04/2013
62139*5^102721-871800Lelio R Paula10/2014
62142^238494-16571794Lelio R Paula02/2012
62152^238389-11090571763Enzo Doria05/2014
6216(145*10^71760-1)/971762Serge Batalov12/2014
62177^84913+506271760Mike Oakes02/2010
6218(F(11446)^31-F(11445)^31)/F(11444)71753Wayne Halsdorf03/2012
62192^238268-9730571726Lelio R Paula05/2012
6220gcd(V(1330365),5*F(266073)*(F(266073)-1)+1)71724Serge Batalov04/2015
62212^238235-11324771716Enzo Doria07/2014
62222*12^66450-5^6645071712Mike Oakes11/2010
6223(2^238213+lucasV(1,2,238213)+1)/471709Mike Oakes11/2016
62242^238199-11181771706Enzo Doria05/2014
6225lucasU(46,1,43125)+lucasU(46,1,43124)71696Mike Oakes04/2009
62262^238144+9876533171689Jason Earls01/2009
622718^57102-426571679Enzo Doria03/2013
6228(73*10^71670-1)/971671Robert Price01/2015
62292^238081+1155*23808171670Henri Lifchitz02/2005
62302^238067-11192571666Enzo Doria05/2014
623136^46030+3571637Norbert Schneider04/2014
6232(74*10^71621+313)/971622Robert Price11/2017
62332^237905-9171617Lelio R Paula02/2012
6234(31*2^237902-1)/12371616Lelio R Paula01/2014
6235(15185*2^237866-1)/4396771605Lelio R Paula04/2015
6236(24737*2^237841+1)/2571601Lelio R Paula06/2014
62372^237846+129971599Lelio R Paula05/2012
62386^92004+19980171594Mike Oakes02/2011
6239159^32516+271581Lelio R Paula05/2013
62402^237781+85571580Lelio R Paula05/2012
62412^237720-407971561Yves Minet06/2011
62422^237698-11094571555Enzo Doria05/2014
62432^237695-11323971554Enzo Doria07/2014
62448*5^102362-971549Lelio R Paula10/2014
6245(4*10^71546-31)/971546Erik Branger05/2011
62462^237650+3771540Lelio R Paula02/2012
624718^56977-439171522Enzo Doria03/2013
6248(22699*2^237565+1)/413663771512Lelio R Paula06/2014
6249((1+sqrt(7)+sqrt(6))^48479-1)*((1+sqrt(7)-sqrt(6))^48479-1)*((1-sqrt(7)+sqrt(6))^48479-1)*((1-sqrt(771512Mike Oakes05/2009
6250(26*10^71503+7)/371504Erik Branger11/2013


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: April, 22 2018 09:48 (Time in France)

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